English

On the number of rich lines in high dimensional real vector spaces

Combinatorics 2021-02-16 v4

Abstract

In this short note we use the polynomial partitioning lemma to strengthen a recent result of Dvir and Gopi about the number of rich lines in high dimensional Euclidean spaces. Our result shows that if there are sufficiently many rich lines incident to a set of points then large fraction of them must be contained in a hyperplane.

Keywords

Cite

@article{arxiv.1412.7025,
  title  = {On the number of rich lines in high dimensional real vector spaces},
  author = {Marton Hablicsek and Zachary Scherr},
  journal= {arXiv preprint arXiv:1412.7025},
  year   = {2021}
}